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Superstatistics properties of q-deformed Morse potential in one dimension

Hassanabadi, H., Sargolzaeipor, S., Chung, W.S.

Published Jan 1, 2018• 0 citations
OpenAlex

Abstract

In this paper, after introducing superstatistics in quantum mechanics, first, the Schrödinger equation in one-dimensional in the presence of q-deformed Morse potential is derived. We use an analytical methodology to calculate the energy eigenvalues. Then the thermodynamic properties of the system are calculated. Furthermore, we report effects of all parameters in the problems on the thermodynamic quantities.

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In this paper, after introducing superstatistics in quantum mechanics, first, the Schrödinger equation in one-dimensional in the presence of q-deformed Morse potential is derived. We use an analytical methodology to calculate the energy eigenvalues. Then the thermodynamic properties of the system are calculated. Furthermore, we report effects of all parameters in the problems on the thermodynamic quantities.
Abstract We discuss the thermodynamic properties of a modified Rosen-Morse potential using the q -deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.
In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.
The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.
In this paper, we introduce the exact solution for the wave function in the presence of potential energy, consisting of combination between q-deformed hyperbolic and exponential function with different argument. The functions we have used in the present communication can be regarded as a generalization of the Arai q-deformed function (modified q-deformed Morse potential). In this context, we have restricted our discussion for some particular cases of the q-deformed hyperbolic functions. This is due to the difficulty for dealing with most of the arguments included in the potential functions. For the most particular cases, the energy eigenfunctions are obtained, and the behavior is also discussed. It has been shown that the wave functions are sensitive to the variation in the value of q-deformed parameter as well as the strength of the potential parameter λ. Furthermore, the energy eigenvalues are also considered for some particular cases where the argument of the exponential function plays a strong role effecting its value.
The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.